An optical method to determine radial temperature and water vapor concentration profiles from a radiating combustion source is presented. Equations for radiance and transmissivity using the random band model with constant line widths and a delta-function distribution for line strengths are written for a hypothetical cylindrically symmetrical source. A numerical iterative technique of solution of these equations for temperature and water vapor concentration from measured radiance and transmittance profiles is presented, utilizing band model parameter data from the literature. Experimental data from a small hydrogen-air burner are used to verify the analytical treatment.